Degree Spectra of Relations on Boolean Algebras

We show that every computable relation on a computable Boolean algebra is either definable by a quantifier-free formula with constants from (in which case it is obviously intrinsically computable) or has infinite degree spectrum.     

Computability-theoretic and proof-theoretic aspects of partial and linear orderings

Szpilrajn’s Theorem states that any partial orderP=〈S,<p〉 has a linear extensionP=〈S,<L〉. This is a central result in the theory of partial orderings, allowing one to define, for instance, the dimension of a partial ordering. It is now natural to ask questions like “Does a well-partial ordering always have a well-ordered linear extension?” Variations of Szpilrajn’s Theorem state, for various (but not for all) linear order typesτ, that ifP does not contain a subchain of order typeτ, then we can chooseL so thatL also does not contain a subchain of order typeτ. In particular, a well-partial ordering always has a well-ordered extension.We show that several effective versions of variations of Szpilrajn’s Theorem fail, and use this to narrow down their proof-theoretic strength in the spirit of reverse mathematics.     

Auger and X-ray photoelectron spectroscopic and electrochemical characterization of titanium thin film electrodes

Auger (AES) and X-ray photoelectron spectroscopic (XPS) characterizations of electrochemically oxidized titanium are described. Surface oxides on thin (200–250 Å) vacuum deposited titanium films were formed under conditions of linear potential scan in 1 N KClO₄, 1 N HClO₄ and 1 N H₂SO₄. Current/voltage, capacitance/voltage and surface conductance/voltage relationships confirmed the irreversible formation of the surface oxide at thickness of 20–30 Å/V, for low applied potentials. Post moretem analysis of the thin films by AES and XPS indicated a mixture of metal and metal oxides (TiO₂, Ti₂O₃, TiO) on each surface, with the higher oxide states predominating on the electrochemically oxidized films. Observation of the L_IIIM_2,3M_4,5, N(E) signal shape in the Auger spectra of the potentially oxidized oxidized films showed a suboxide TiO-like surface rather than an TiO₂ surface state. Deconvolution of the $\text{Ti}\text{(2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext><mtext>,\; </mtext><mtext>3</mtext><mtext>2</mtext>}}\text{)}\text{XPS}$ spectra confirmed the coexistence of multiple oxidation states of Ti during electrochemical or atmospheric oxidation of the films. Ion sputtering of each surface was used to characterize the subsurface metal/metal oxide composition and to correlate the oxygen to metal atomic ratio with electrochemical pretreatment.     

There is no degree invariant half-jump

We prove that there is no degree invariant solution to Post's problem that always gives an intermediate degree. In fact, assuming definable determinacy, if is any definable operator on degrees such that on a cone then is low or high on a cone of degrees, i.e., there is a degree such that for every or for every .

     

Ion flotation studies of the chlorocomplexes of some platinum group metals

The anionic chlorocomplexes of Au(III), Pt(IV), Pd(II), Ir(IV), Ir(III) and Rh(III) can be floated from aqueous solutions with cationic surfactants of the type RNR'₃Br. The flotation behavior of each metal is reported with respect to variations of hydrochloric acid and sodium chloride concentrations, the R and R' chain lengths, initial surfactant concentrations and initial metal ion concentrations. The flotation behavior of the metals is compared to the anion-exchange selectivity coefficients and a flotation selectivity sequence of Au(III) > Pt(IV), Ir(IV), Pd(II) > Ir(III) > Rh(III) is generally observed. Nearly 100% of Au(III), Pt(IV), Ir(IV) and Pd(II) can be recovered from dilute solutions using the ion flotation procedures.